QUADRATICS

QUADRATICS

1. Formulas

   • Standard Form
     • y=ax^2+bx+c
       • Find y- intercept
         • "c"
       • Find zeros
         • Quadratic formula
   • Vertex Form
     • y=a(x-h)+k
       • Find vertex, and AOS
         • Optimal value
           • k
       • Translations/ Transformations
         • "a"
           • Stretches
             • lal>1
               • Vertically stretches by factor of lal
           • compression
             • 0<lal<1
               • Vertically compresses by factor of lal
           • Reflection
             • a<0
               • Reflected in x-axis
         • "h"
           • h>0
             • Horizontally translated to the right by lhl
           • h<0
             • Horizontally translated to the left by lhl
         • "k"
           • k>0
             • Vertically translated up by lkl
           • k<0
             • Vertically translated down by lkl
   • Factored Form
     • y=a(x-s)(x-t)
       • Find zeros/roots/x-intercepts
         • set y 0

2. Determining the number of roots

   • "a" and "k" have the same signs
     • No roots
   • "a" and "k" have different signs
     • two roots
   • "a" is irrelevant and k is not zero
     • One root

3. Graphing

   • 1. Start with y=x^2 and transform all points
     • base formula
   • 2. Plot the vertex and use new step pattern for other points
     • New step pattern= original step pattern (1,3,5) times "a"

4. Completing squares

   • To convert an equation to a vertex form
   • y=ax^2 + bx +c
     • perfect squares
       • b
   • word problems
     • Ask for max/min, or the x value that give the max/min

5. Factoring

   • 2 terms
   • 3 terms
   • 4 terms